Inequality/equality constrained optimization: a quadratically and globally convergent feasibility method

We present an analytical robustness comparison of two methods for inequality/equality constrained optimization or nonlinear programming. The methods compared are (1) a feasibility method (FM) and (2) rudimentary sequential quadratic programming with an L1 merit function (L1-SQP). We then also make note of a global convergence result (similar to that of FM) for a new filter-type SQP algorithm. We claim no analytical robustness advantage of FM over the filter-type SQP algorithm. The problem statement assumptions include non-stationarity of constraint error norms except at zero constraint error, without which we are not aware of any algorithm that is guaranteed to converge to a tolerance-feasible stationary point of a penalty function or a Kuhn-Tucker point. Global and quadratic convergence of FM is proved analytically. Rudimentary L1-SQP is shown to exhibit potential failure even from a feasible starting point, due to an onset of infeasible sub problems.